I read that Galois group is a permutation of the zeros or roots, this is new to me, so, I have a question.
How can I prove, all roots of a polynomial are permutation of one another?
in other words, all roots has symmetric therefore, there is no asymmetric root (by asymmetric root, I mean a root which is not a permutation of another root) for a given polynomial.
I guess there is a relation between the proof and elementary symmetric polynomials but I can't go far.
Thanks.